This paper is concerned with the linear elastic static analysis of thin arbitrary shell structures by the use of the displacement approach finite element method. The various factors involved in selecting a shell finite element are discussed. A comprehensive formulation of a 27 degree of freedom, arbitrary, doubly-curved, nonconforming, triangular, shallow shell element is presented. Both the normal and tangential displacement fields are expressed by "incomplete" cubic, natural coordinate, polynomial interpolation functions. A WATFIV/FORTRAN computer code utilizing this element in a linear elastic static analysis of thin shell structures is formulated and presented. Demonstration problems are presented and comparisons are made with solutions in the literature. / Master of Science